Computational contact mechanics has been developed into a separated branch of computational mechanics during the last decades. A fairly large number of publications including several monographs on computational contact mechanics has been published since then. Modeling of contact interactions became fairly standard in numerous finite element software packages available for engineers. Various aspects of the numerical solution has been polished by many researchers. One of the important aspects, even though being obvious for everyone, – the geometrical treatment of the contact – is often remains hidden inside the computational algorithm. Contact interaction from a geometrical point of view can be seen as interaction between deformable surfaces possessing various geometrical features such as surfaces, edges and vertexes. This monograph aims on the development of the unified geometrically exact formulation of contact algorithm for various possible geometrical situations of contacting bodies: surface-to-surface, curve-to-surface etc. Known computational contact algorithms will be reconsidered in accordance with the geometry of contacting bodies in a form independent of their approximation, in the so-called covariant form. This combination forms the geometrically exact theory of contact interactions .
In order to locate this development in computational contact mechanics focusing on its computational issues and formulate the goals of the current book, first, we try to classify these developments.
KeywordsContact Interaction Contact Pair Augmented Lagrangian Method Contact Algorithm Covariant Approach
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